POJ 1679 the unique MST "MST is the only, prime algorithm, the best code"

The Unique MST

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 27389		Accepted: 9816

Description

Given a connected undirected graph, tell if it minimum spanning tree is unique.

Definition 1 (Spanning Tree): Consider a connected, undirected graph G = (V, E). A spanning tree of subgraph of g, say T = (V ', E '), with the following properties:
1. V ' = v.
2. T is connected and acyclic.

Definition 2 (Minimum Spanning Tree): Consider an edge-weighted, connected, undirected graph G = (V, E). The minimum spanning tree T = (V, E ') of G is the spanning tree, which has the and the smallest total cost. The total cost of T means the sum of the weights on all the edges in E '.

Input

The first line contains a single integer t (1 <= t <=), the number of test cases. Each case represents a graph. It begins with a line containing, integers n and m (1 <= n <=), the number of nodes and edges. Each of the following m lines contains a triple (xi, Yi, WI), indicating that Xi and Yi is connected by an edge with Weig HT = wi. For any of the nodes, there is at the most one edge connecting them.

Output

For each input, if the MST was unique, print the total cost of it, or otherwise print the string ' not unique! '.

Sample Input

23 31 2 12 3 23 1 34 41 2 22 3 23 4 24 1 2

Sample Output

3Not unique!

Source

POJ monthly--2004.06.27[email protected]

Original title Link: http://poj.org/problem?id=1679

Test instructions: Look at the smallest spanning tree is unique, the Web read a lot of code, all use the enumeration, but found a code without enumeration,

Original link: http://blog.csdn.net/cambridgeacm/article/details/7857252, but one thing does not understand, is why the main loop is n times, not n-1 times. Is there a great God, you know?

AC Code:

#include <iostream> #include <cstdio> #include <cstring>using namespace std;const int inf=0x3f3f3f3f;         int a[105][105];int dis[105];bool vis[105];int n,m;void Prime () {for (int i=1; i<=n; i++) {dis[i]=a[1][i];    Vis[i]=false;    } int ans=0;    BOOL Flag=false;        for (int i=1; i<=n; i++) {int minn=inf;        int p=-1;        for (int j=1; j<=n; J + +) {if (!vis[j]&&dis[j]<minn) minn=dis[p=j];        } int k=0;        for (int j=1; j<=n; J + +) {if (Vis[j]&&a[p][j]==minn) k++;            } if (k>1) {flag=true;        Break        } vis[p]=1;        Ans+=minn;        for (int j=1; j<=n; J + +) {if (!vis[j]&&dis[j]>a[p][j]) dis[j]=a[p][j]; }} if (flag) cout<< "Not unique!"    <<endl; else Cout<<ans<<endl;}   int main () { int T;    Freopen ("Data/1679.txt", "R", stdin);    cin>>t;        while (t--) {cin>>n>>m;                for (int i=0, i<=n; i++) {for (int j=0; j<=n; J + +) if (i==j) a[i][j]=0;        else A[i][j]=inf;        } int x, y, Z;            while (m--) {scanf ("%d%d%d", &x,&y,&z);        if (Z<a[x][y]) a[x][y]=a[y][x]=z;    } Prime (); } return 0;}

POJ 1679 the unique MST "MST is the only, prime algorithm, the best code"